Question

How do you write an equation in point-slope form for the line through the given slope:(4,-6); m=3/5?

Answer 1

Gradient (`m`)`=3/5`
Coordinates located on the line: `(4,-6)`
`4` is the x-coordinate while `-6` is the y-coordinate

Remember the general linear equation of `y=mx+c`

We can use the method of substitution to find the y-intercept (c) in the linear equation first.
As we substitute the coordinates & gradient in the general linear equation of `y=mx+c` ... We get:
`-6=3/5`x`4` `+c`
`-6=12/5` `+c`
`-6-12/5=` `c`
`-42/5=` `c`
`c=-42/5=-8.4`

Now that we know the y-intercept (c) of the linear equation, we can form the linear equation by adding the gradient and y-intercept into the general equation of `y=mx+c`.

Thus, the linear equation would be `y=3/5x-8.4`